Neutron Star Magnetic Mountains: An Improved Model Maxim Priymak Supervisor: Dr. A. Melatos Orange 2009: Pulsar Meeting

Overview Accreting Neutron Stars (NS) as Gravitational Wave (GW) sources Magnetic mountain mechanism Improved magnetic mountain model –Implemented more realistic EoS GW detectability decreases Motivation –Quantify GW detectability of accreting NS by LIGO/ALIGO –Construct GW search templates –Infer NS properties (M accreted, conductivity etc…)

Accreting Neutron Stars Accreting Neutron Stars (NS) X-ray sources (LMXB/HMXB) NS spin up NS spin measurements: X-ray pulsations/Burst oscillations/QPO Spin distribution cut off > 700 Hz None at ≈ Ω break up (~ Hz) NOT a selection effect 2 mechanisms explain this: 1)Gravitational Wave (GW) emission 2)Propeller effect Dominant mechanism Inconclusive –both contribute From tabulated data of Watts et al ? XTE J ? X-ray pulsations Burst oscillations Quasi-Periodic Oscillations

Magnetic Mountain Accretion driven (LMXB/HMXB) B confines matter: 1) P HYDROSTATIC > P MAGNETIC Matter Spreads 2) B distorted Equilibrium NS asphericity 4) Spin/Dipole axes misaligned Q ≠ 0 GW Advantages (as GW emitter): – Known position and/or signal f (X-ray / Optical / Radio) + Persistent Current Models: – 2D (Payne & Melatos 2004) Axisymmetric MHS equilibrium Stable – 3D (Vigelius & Melatos 2008) Non-ideal MHD Stable Time evolution of 3D magnetic mountain Vigelius & Melatos 2008 Current model deficiencies: – Rigid crust no sinking – Irrotational no F CORIOLIS – Constant BC’s no crustal freezing – Isothermal no variable resistivity – No inclination unrealistic – Ideal isothermal EoS (P = c s 2 ρ) unrealistic

Solving the MHS equilibrium ψ1ψ1 ψ5ψ5 ψ4ψ4 ψ3ψ3 ψ2ψ2 ψ6ψ6 ψ7ψ7 ψ8ψ8 ψ9ψ9 ψ 10 ψ1ψ1 ψ7ψ7 ψ6ψ6 ψ5ψ5 ψ4ψ4 ψ3ψ3 ψ2ψ2 ψ9ψ9 ψ8ψ8 Initial State Final State Supplemented with: –EoS: –Mass-flux Constraint: dM/dΨ| final = dM/dΨ| initial + dM/dΨ| accreted Gravitational force Lorentz force (pressure + tension) Pressure gradient Net Force

MHS Equilibrium: Dipole Moment (μ) and Ellipticity (ε) versus M accreted 2 Feasible EoS: (P = Kρ Γ ) –Degenerate Neutron EoS [K = 5.4e4 (SI), Γ = 5/3] –Relativistic Degenerate Electron EoS [K = 4.9e9 (SI), Γ = 4/3] (cf. Ideal Isothermal EoS P = c s 2 ρ )

MHS Equilibrium: |B| max and ρ max versus M accreted 1)Attained ρ max realistic (cf. Ideal Isothermal EoS) 2)Above B cracking plastic flow ?

Magnetic Mountain: Ideal Isothermal EoS M accreted = 3.3x10 -5 M סּ

M accreted = 3.3x10 -7 M סּ M accreted = 3.3x10 -8 M סּ Degenerate n EoS: Degenerate Relativistic e - EoS: Magnetic Mountain: Adiabatic EoS

LIGO/ALIGO Estimates GW strain h is: LIGO locations Vigelius et al LIGO/ALIGO detectability curves Relativistic Degenerate e - EoS Degenerate n EoS M a = M סּ M a = M סּ M a = M סּ M a = M סּ M a = M סּ M a = M סּ No observed NS that spin fast enough Ohmic diffusion arrests mountain growth

Current Work Extend to realistic M accreted Implement Realistic Nuclear EoS Future Work Crustal freezing / sinking Compute feedback b/w mountain and magnetosphere Cornell Collaboration Application to X-ray bursts –Light curves & cyclones / Episodic decay of the mountain WHY? –Quantify the effects on GW detectability by LIGO/ALIGO –Construct GW search templates –Infer NS properties (M accreted, conductivity etc…)

The End Thank you for your attention. Any Questions?